Stochastic starting designs

[mdlerch]

Related to #2. Using largest leverage will always produce the same starting design. We should add some stochasticity to this so we don't always start at the same point, thus, hopefully exploring the design space more efficiently.

[mdlerch]

Hey @joncheryl , what do you think of this. Right now we run through the fedorov process once with iter iterations. How about we run through the fedorov process multiple times each of iter iterations. To start the fedorov process, the first time we straight up use largest leverage and the subsequent times we use some large leverage points and some random points.

[joncheryl]

I don't know if you noticed but I changed the initial design function so that the initial design contains the r largest leverage points (where r is the rank of the design matrix) and the rest are randomly selected from the candidate set. A think that a design with only the largest leverage points will have a lot of points on the boundary and this may not be best. I like the idea of running the federov process several times with different initial designs so as to better explore the design space. I should probably reread that jobo paper again.

I was thinking that maybe a good initial design would be the least dense design as possible, i.e. one that maximizes the minimum distance between points. This may be possible to generate by systematically selecting from leverage quantiles (dubious). For example, first select the points with the largest leverage (maybe a few have leverage 1), then select the points with the smallest leverage (maybe a few have leverage 0), then select the points with the median leverage, then points with the 75th percentile leverage, then points with the 25th percentile leverage, then points with the 87.5th percentile leverage, then points with the 12.5th percentile leverage, 62.5th percentile, etc.

[mdlerch]

I did notice your changes--which I thought were a very good idea. I
think that since these are leverages in model space they won't
necessarily be all be on the "edge" of the design space, but they
probably will tend that way. For "D" criterion, all points on some sort
of edge is probably a good thing anyway.

It might be smart to utilize different initialization routines depending
on which criterion is chosen. For example, max leverage for "D" and the
"spread out leverages" that you are talking about for "G" or "I".

On Tue, Dec 30, 2014 at 07:48:57PM -0800, John Sherrill wrote:

I don't know if you noticed but I changed the initial design function
so that the initial design contains the r largest leverage points
(where r is the rank of the design matrix) and the rest are randomly
selected from the candidate set. A think that a design with only the
largest leverage points will have a lot of points on the boundary and
this may not be best. I like the idea of running the federov process
several times with different initial designs so as to better explore
the design space. I should probably reread that jobo paper again.

I was thinking that maybe a good initial design would be the least
dense design as possible, i.e. one that maximizes the minimum distance
between points. This may be possible to generate by systematically
selecting from leverage quantiles (dubious). For example, first select
the points with the largest leverage (maybe a few have leverage 1),
then select the points with the smallest leverage (maybe a few have
leverage 0), then select the points with the median leverage, then
points with the 75th percentile leverage, then points with the 25th
percentile leverage, then points with the 87.5th percentile leverage,
then points with the 12.5th percentile leverage, 62.5th percentile,
etc.

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